If \(U=\{1,2,\ldots,10\}\), \(A=\{1,2,3,4\}\), and \(B=\{3,4,5,6\}\), what is \(A'\Delta B'\) equal to?
Answer and explanation
Correct answer: \(A\Delta B\)
For any two subsets of the same universal set, taking complements does not change which elements belong to exactly one of the sets. Algebraically, \(A'\Delta B'=(A'\cap B)\cup(B'\cap A)=A\Delta B\). Here \(A\Delta B=\{1,2,5,6\}\), since these elements occur in exactly one of A and B. Therefore, A is correct.
Frequently asked questions
What is the correct answer to this question?
\(A\Delta B\)
Why is this the correct answer?
For any two subsets of the same universal set, taking complements does not change which elements belong to exactly one of the sets. Algebraically, \(A'\Delta B'=(A'\cap B)\cup(B'\cap A)=A\Delta B\). Here \(A\Delta B=\{1,2,5,6\}\), since these elements occur in exactly one of A and B. Therefore, A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
